In this article, we propose an efficient and accurate compressive-sensing-based method for estimating the light transport characteristics of real-world scenes. Although compressive sensing allows the efficient estimation of a high-dimensional signal with a sparse or near-to-sparse representation from a small number of samples, the computational cost of the compressive sensing in estimating the light transport characteristics is relatively high. Moreover, these methods require a relatively smaller number of images than other techniques although they still need 500-1000 images to estimate an accurate light transport matrix. Precomputed compressive sensing improves the performance of the compressive sensing by providing an appropriate initial state. This improvement is achieved in two steps: 1) pseudo-single-pixel projection by multiline projection and 2) regularized orthogonal matching pursuit (ROMP) with initial signal. With these two steps, we can estimate the light transport characteristics more accurately, much faster, and with a lesser number of images.